Find the temperature at each of the six positions given at the moment t = 150 se

Question

Find the temperature at each of the six positions given at the moment t = 150 seconds.

The heat diffusion equation for transient, one-dimensional radial conduction in a long, solid cylinder is; Suppose ro is the cylinder and the surface is exposed to a convection environment with fluid temperature T and convection coefficient h, The boundary conditions are:- Suppose the cylinder is .initially at uniform temperature T(r, 0) = T1. The dimensionless form of this. equation, its. initial condition, and its boundary conditions are; Figure 5.S in-section- 5.4 of the, text has a temperature response, chart for the solutions to this problem. Use the chart to solve the following problem: A long' 100-mm diameter steel cylinder -is initially, at uniform temperature

Explanation / Answer

Fo = alpha*t/L^2 = K*t/(rho*Cp*L^2)

Fo = 38*150/(7800*485*0.1^2)

Fo = 0.15

Bi = h*L/K = 1500*0.1/38

Bi = 4

Ti = 200

Tinf = 50

1)

x/L = 0

(T - Tinf)/(Ti-Tinf) = 1

Therefore

T =200

2)

x/L = 0.2

(T - Tinf)/(Ti-Tinf) = 0.99

Therefore

T = 198.5

3)

x/L = 0.4

(T - Tinf)/(Ti-Tinf) = 0.99

Therefore

T = 198.5

4)

x/L = 0.6

(T - Tinf)/(Ti-Tinf) = 0.95

Therefore

T = 192.5

5)

x/L = 0.8

(T - Tinf)/(Ti-Tinf) = 0.9

Therefore

T = 185

6)

x/L = 1

(T - Tinf)/(Ti-Tinf) = 0.85

Therefore

T = 177.5

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